UC-MRLF 


The  First  Deslandres'  Group  of  the 
Positive  Band  Spectrum  of  Nitro- 
gen, under  High  Dispersion 


A  THESIS 

SUBMITTED   FOR   THE  DEGREE   OF   DOCTOR 
OF   PHILOSOPHY 


RAYMOND  T.  BIRGE 


IXIVERSITY  OF  WISCONSIN 
'9*3 


The  First  Deslandres5  Group  of  the 
Positive  Band  Spectrum  of  Nitro- 
gen, under  High  Dispersion 


A  THESIS 

SUBMITTED  FOR  THE  DEGREE  OF  DOCTOR 
OF  PHILOSOPHY 


BY 

RAYMOND  T.  BIRGE 


UNIVERSITY  OF  WISCONSIN 
1913 


THE  FIRST  DESLANDRES'   GROUP  OF  THE  POSITIVE 

BAND  SPECTRUM  OF  NITROGEN,  UNDER  HIGH 

DISPERSION 

BY  RAYMOND  T.  BIRGE 

This  paper  is  a  preliminary  discussion  of  the  First  Deslandres' 
Group  of  the  band  spectrum  of  nitrogen,  based  mainly  upon  photo- 
graphs taken  by  the  author  in  the  second  order  of  a  21 -foot 
concave  grating,  from  \5ooo  to  \68oo.  The  bands  are  almost 
completely  resolved  into  lines,  and  the  discussion  in  this  paper  is 
concerned  with  the  relations  between  the  lines  forming  the  three 
principal  heads  of  the  bands. 

INTRODUCTION 

The  positive  band  spectrum  of  nitrogen  has  been  the  subject 
of  a  large  number  of  investigations.  Under  low  dispersion  the 
apparent  regularity  of  the  bands,  both  in  position  and  in  appear- 
ance, is  very  striking.  The  violet  end  of  this  spectrum  can  easily 
be  photographed  under  high  dispersion,  but  because  of  the  rela- 
tively low  intensity  in  the  longer  wave-lengths,  this  portion  had 
not  previously  been  resolved  into  its  component  lines  in  a  satis- 
factory manner.  Von  der  Helm1  made  the  latest  attempt.  The 
two  objects  of  his  investigation,  with  his  success  in  accomplishing 
them,  are  stated  as  follows: 

1.  tlbersicht  iiber  den  gesamten  Teil  des  in  Frage  kommenden  Spectrums, 
inbesondere  iiber  die  Lage  der  Bandenkopfe. 

2.  Genaueres  Studium  einzelner  Banden. 

Den  ersten  Teil  der  Aufgabe  darf  ich  als  gelost  betrachten;  am  zweiten 
bin  ich  leider  fast  vollig  gescheitert. 

Von  der  Helm  gives  a  complete  discussion  of  relevant  previous 
work  on  nitrogen,  together  with  the  possible  results  of  such  an 
investigation,  and  the  first  eight  pages  of  his  article  could  well 
form  the  introduction  to  this  paper. 

The  First  Deslandres'  Group  of  bands  extends  from  X  5100 
out  into  the  infra-red.  Measurements  on  the  heads  of  individual 

1  Zeitschr.  f.  wiss.  Phot.,  8,  405,  1910. 

50 


GIFT 


POSITIVE  BAND  SPECTRUM  OF  NITROGEN  51 

bands  have  previously  been  made  to  X  9100.  The  results  seem  to 
show  that  the  spectrum  consists  of  a  series  of  band  groups,  each 
of  which  is  most  intense  at  the  center,  and  diminishes  in  intensity 
toward  either  side.  Kayser's  Handbuch*  gives  only  three  groups, 
which  he  calls  a,  b,  and  c.  Other  groups  of  longer  wave-length 
have  since  been  found,  arid  it  appears  now  that  there  are  six  groups 
in  all,  which  will  be  designated  a  to  /  respectively. 

Group  a  i  .  06  /A  (?) 

Group  b  9101  (  ?)  to  7887 

Group  c  7887  to  7059 

Group  d  7059  to  6185  (Kayser's  a  group) 

Group  e  6186  to  5485  (Kayser's  b  group) 

Group/  5632  to  5126  (Kayser's  c  group) 

Group  /is  quite  different  from  the  others.  It  has  two  intensity 
maxima,  one  at  X  5200  and  the  other  at  X  5475.  This  would  indi- 
cate two  groups,  but  as  the  spacing  is  the  same  in  both,  it  has  been 
customary  to  classify  them  together.  This  group  also  overlaps 
considerably  on  group  e. 

The  author  obtained,  besides  the  exposures  on  the  large  grating, 
one  on  a  Hilger  constant  deviation  spectroscope,  extending  to 
X  7650.  From  this  point  to  X  9100  we  have  only  the  measurements 
of  Croze.2  Coblentz,3  in  connection  with  other  infra-red  work,  has 
recorded  positions  of  maximum  intensity  at  0.546,  0.667,  °-75> 
0.90,  and  i.o6ju.  These  are  very  evidently  the  approximate 
positions  of  maximum  intensity  in  the  several  band  groups.  The 
reading  at  i  .  06  ju  points  to  the  existence  at  this  point  of  another 
group,  which  we  have  called  group  a. 

In  making  this  investigation  the  author  had  two  objects  in 
view:  (i)  to  determine  whether  or  not  the  bands  in  any  one  group 
were  identical;  (2)  to  determine,  in  case  there  were  any  similarities, 
whether  corresponding  lines  in  successive  bands  would  fit  into  a 
Deslandres'  series  or  other  arithmetical  relation. 

The  results  of  the  study  made  thus  far  indicate  that  out  of  the 
250  or  more  lines  composing  each  band,  at  least  50  of  the  strongest 
are  related  to  corresponding  lines  in  other  bands,  and  that  the 
relationship  is  approximately  that  expressed  by  Deslandres'  Law: 


1  Handbuch  der  Spectroscopie,  5,  828. 

2  Comptes  rendus,  150,  860,  1910.  3  Physical  Review,  22,  i,  1906. 


629 


52  RAYMOND  T.  BIRGE 

where  a,  b,  and  c  are  constants,  and  m  takes  successive  integral 
values. 

EXPERIMENTAL  ARRANGEMENTS 

Atmospheric  nitrogen,  free  from  oxygen,  carbon  dioxide,  and 
water- vapor,  was  used  as  a  source.  Hence  the  inert  gases  of  the 
atmosphere  were  present,  but  the  only  lines  due  to  them  which 
have  thus  far  been  noted  are  a  few  of  the  stronger  argon  lines  of  the 
red  spectrum.  There  is  no  trace  of  helium  X  5876.  Traces  of 
mercury  diffused  into  the  spectrum  tube  from  the  pressure  gauge, 
but  only  the  three  strong  lines  at  X  5790,  X  5769,  and  X  5461 
appear,  the  last  enormously  overexposed. 

The  nitrogen  was  electrically  excited  in  a  Goetze  "Type  C' 
spectrum  tube.  The  emission  from  the  capillary  of  such  a  tube, 
in  a  " head-on"  direction,  appears  to  be  the  most  intense,  per 
unit  cross-section,  now  obtainable.  The  electrical  excitation  was 
furnished  by  the  secondary  of  a  large  induction  coil,  the  primary 
being  run  on  no  volts  A.C.,  1.5  amperes.  The  nitrogen  was 
introduced  at  about  5  mm  pressure  and  used  until  the  pressure 
fell  to  about  i  mm,  low  enough  to  cause  a  slight  diminution  of 
the  radiation.  Refilling  of  the  tube  was  necessary  only  once  in 
24  to  36  hours. 

The  tube  was  placed  accurately  "head-on"  to  the  slit  of  the 
grating,  60  cm  away.  A  double  convex  lens  of  15  cm  focus  pro- 
duced on  the  slit  a  sharp  image  of  the  end  of  the  capillary,  some- 
what more  than  i  mm  in  diameter.  This  usual  arrangement  was 
now  varied  by  introducing,  at  a  distance  of  12  cm  from  the  slit, 
a  double  concave  cylindric  lens  of  1 2  cm  focus,  placed  with  its  axis 
horizontal.  This  caused  the  circular  image  on  the  slit  to  be  drawn 
out  into  a  vertical  line  some  2  cm  in  length.  The  use  of  such  a 
cylindric  lens  in  spectrum  work  has  been  advocated  by  Humphreys,1 
but  I  know  of  no  definite  statement  of  the  advantages  and  disadvan- 
tages incident  to  its  use. 

The  action  of  the  cylindric  lens  is  greatly  to  reduce  the  vertical 
aperture  of  the  cone  of  rays  proceeding  from  the  slit.  With  the 
particular  lenses  used,  it  is  possible,  with  a  source  of  light  less  than 
approximately  2  mm  in  diameter,  to  reduce  the  vertical  aperture, 
at  the  grating,  to  less  than  the  length  of  the  grating  rulings.  Thus 

1  Astrophysical  Journal,  18,  324,  1903. 


POSITIVE  BAND  SPECTRUM  OF  NITROGEN  53 

the  cross-section  of  the  cone  of  light  at  the  grating,  instead  of  being 
a  75-cm  circle,  is  reduced  (roughly)  to  an  ellipse  of  75  cm  horizontal 
diameter,  but  with  a  vertical  diameter  of  5  cm  or  less.  The  gain 
in  intensity  of  the  middle  point  of  the  astigmatic  image  at  the 

camera  is   theoretically  — =15.     The  actual  increase,  deter- 

5  cm 

mined  experimentally,  was  thirteen  fold. 

If  now  the  source  is  made  4  mm  in  diameter,  instead  of  2,  the 
amount  of  light  actually  striking  the  grating,  using  the  cylindric 
lens,  is  scarcely  increased  at  all.  But  with  the  ordinary  arrange- 
ment, the  amount  would  practically  be  doubled.  Hence  the 
advantage  of  the  cylindric  lens  is  proportionally  decreased.  For 
sources  more  than  2  cm  in  diameter,  there  is  no  appreciable  advan- 
tage in  using  a  cylindric  lens. 

The  chief  disadvantage  attendant  upon  its  use  is  the  necessity 
of  accurate  adjustment.  The  centers  of  the  tube,  convex  lens, 
concave  lens,  and  slit  should  all  lie  accurately  in  the  horizontal 
plane  formed  by  the  center  of  the  grating  and  of  the  camera.  With 
this  condition  fulfilled,  and  the  cone  of  light  falling  symmetrically 
upon  the  grating,  a  raising  or  lowering  of  the  cylindric  lens  of  even 
one-tenth  of  a  millimeter  is  sufficient  to  throw  an  appreciable  por- 
tion of  the  light  entirely  below  or  above  the  rulings  of  the  grating. 

Because  of  the  excess  of  radiation  in  a  " head-on"  direction, 
the  illumination  of  the  grating  is  far  from  uniform;  but  this  is  true 
even  when  the  cylindric  lens  is  not  used.  Such  a  non-uniformity 
is  liable,  however,  to  cause  a  shift  of  the  lines  of  the  comparison 
spectrum  relative  to  those  under  investigation.  The  actual  shifts 
found  in  many  cases,  between  the  iron  and  nitrogen  lines,  are 
believed  to  be  due  primarily  to  this  cause. 

As  a  comparison  source  I  used  an  iron  arc  of  the  Pfund1  type, 
run  on  200  volts,  5  amperes,  with  iron  and  carbon  electrodes.  It 
worked  in  a  very  satisfactory  manner.  The  exposures  were  made 
in  the  second  order,  and  both  the  second-order  and  coincident  third- 
order  international  iron  normals  were  used,  the  measurements  in 
the  ultra-violet  being  those  of  Buisson  and  Fabry,2  not  yet  offi- 
cially adopted  as  standards. 

No  relative  shift  of  orders  could  be  detected  on  those  plates 
where  both  the  second-  and  third-order  normals  were  present. 

1  Astro  physical  Journal,  27,  296,  1908.  *  Ibid.,  28,  169,  1908. 


54  RAYMOND  T.  BIRGE 

Whenever  two  normals  fell  near  together  and  were  both  of  suitable 
intensity  for  an  accurate  setting,  the  agreement  was  perfect. 
When  one  or  both  lines  were  overexposed  the  disagreement  might 
be  anything  from  0.007  A  down.  This  was  taken  to  indicate 
that  the  secondary  international  normals,  when  overexposed,  do 
not  necessarily  broaden  symmetrically.  The  much  greater  uni- 
formity in  intensity  of  the  normals  between  X  3500  and  X  4500  thus 
makes  them  preferable  for  use,  and  this  fact,  coupled  with  the  great 
faintness  of  the  normals  from  X  5900  into  the  red,  caused  the  author 
to  use  only  the  coincident  third-order  normals  in  the  region  X  5900 
to  X  6800. 

In  order  to  eliminate  the  exceedingly  strong  violet  bands  of 
nitrogen,  an  8  per  cent  solution  of  potassium  chroma te  5  mm  thick 
was  employed.  The  absorption  of  this  solution  sets  in  at  about 
X  5200  and  this  accounts  for  the  rapid  decrease  in  intensity  below 
this  point.  (See  Plate  III.)  Although  the  head  of  the  \3576 
band  is  a  thousand  times  as  intense,  photographically,  as  that  of 
any  band  under  investigation,  no  trace  of  it  appears  on  the  exposures. 
Fluorescein  was  tried  as  an  absorbent  and  found  quite  ineffective. 

For  the  exposures  from  X  5000  to  X  5900  the  Cramer  Instanta- 
neous Isochromatic  plates  were  employed,  while  from  X  5800  to 
X  6900  both  Cramer  " Spectrum"  and  Wratten  &  Wainwright  "A" 
Panchromatic  were  used.  For  the  one  exposure  on  the  Hilger 
spectroscope,  from  X  6800  to  X  7700,  I  used  a  Wratten  &  Wain- 
wright "B"  Panchromatic  plate. 

The  strongest  portion  of  the  spectrum,  from  the  photographic 
standpoint,  is  that  from  X  5700  to  X  5800.  The  X  5804  band  is 
fully  three  times  as  intense  as  that  at  X6623,  the  only  one  which 
von  der  Helm  appears  to  have  obtained  sufficiently  intense  for  meas- 
urement. The  region  from  X  5500  to  X  5900  was  accordingly 
photographed  first,  using  12X1^  inch  plates,  and  the  usual  Row- 
land type  of  comparison  shutter.  All  other  exposures  were  made 
with  18X2^  inch  plates,  using  a  comparison  shutter,  mounted 
independent  of  the  camera. 

In  making  exposures  several  days  in  length,  the  greatest  prob- 
lem is  a  proper  control  of  temperature.  Fortunately  for  the  author, 
the  large  grating  of  the  University  of  Wisconsin  is  mounted  inside  a 
double-walled  room,  built  in  turn  entirely  inside  an  ordinary  room. 


POSITIVE  BAND  SPECTRUM  OF  NITROGEN  55 

The  temperature  in  this  outer  room  was  kept  constant  within  a 
few  tenths  of  a  degree  by  suitable  electrical  heating.  This  enabled 
the  temperature  of  the  grating  to  be  kept  constant  within  a  few 
hundredths  of  a  degree.  The  grating  temperature  was  read  on  an 
accurate  mercury  thermometer,  mounted  in  metallic  contact  with 
the  side  of  the  grating.  Other  thermometers  were  laid  in  a  slot 
in  the  iron  beams  forming  the  slit-grating-camera  triangle.  A 
small  change  of  temperature  in  this  triangle  is  immaterial,  so  long 
as  all  parts  remain  at  an  equal  temperature. 

For  the  grating,  however,  a  constant  temperature  is  indis- 
pensable, the  change  of  wave-length  at  a  given  point  on  the  camera 
plate  being  proportional,  to  first-order  effects,  to  the  change  in 
the  width  of  the  grating  space.1  Holtz2  seems  to  question  this,  and 
spends  some  time  searching  for  other  causes  for  the  observed  shift 
of  lines  with  temperature.  The  mounting  of  the  grating  at  the 
University  of  Wisconsin  is  such  as  to  exclude  the  chief  sources  of 
error  which  he  mentions,  and  it  was  found  experimentally  that  the 
shift  was  exactly  that  computed  from  the  change  of  temperature 
and  the  coefficient  of  expansion  of  the  grating. 

A  change  of  o?oi  C.  in  the  grating  temperature  will  shift  a 
line  (at  X  5000)  about  o .  ooi  A.  During  the  exposures  the  tempera- 
ture was  never  allowed  to  leave  a  o?i  C.  range,  and  during  any 
one  exposure  the  average  variation  from  the  mean  temperature 
varied,  in  different  exposures,  from  o?oi5  to  o?o35  C.  The 
broadening  of  the  lines  was  thus  always  less  than  o.oi  A. 

Not  only  the  temperature,  but  the  barometric  pressure  as  well, 
causes  a  shift  of  the  spectrum.  A  change  of  i  mm  in  pressure  will 
shift  the  lines  0.002  A.  With  frequent  total  pressure  variations 
of  2  cm,  sufficient  to  cause  a  0.04  A  broadening  of  the  lines,  it 
becomes  necessary  to  eliminate  this  change  also.  This  was  done 
by  arbitrarily  changing  the  temperature.  A  i  cm  rise  of  pressure 
is  compensated  by  a  o?i5  lowering  of  temperature.  The  mean 
temperature  mentioned  above,  which  I  endeavored  to  hold  con- 
stant, refers  to  the  initial  temperature,  properly  corrected  for 
subsequent  change  in  barometric  pressure. 

The  time  of  exposure  varied  from  66  to  120  hours.     The  slit- 

'See  Baly,  Spectroscopy,  p.  241,  1912  edition. 
2  Zeitschr.  /.  Wiss.  Phot.,  12,  101,  1913. 


56  RAYMOND  T.  BIRGE 

width  varied  from  o.oi  to  0.04  mm,  being  usually  0.02  mm.  The 
theoretical  resolving  power  of  the  grating  (a  6-inch,  14, 43 8-line 
grating),  for  the  slit- width  used,  was  actually  obtained  on  all 
exposures  except  those  in  the  red  where,  in  the  second  order,  the 
grating  has  a  somewhat  poorer  definition. 

The  spectrum  was  photographed  on  eight  different  plates,  two 
for  each  region.  These  regions  were  (i)  X  6goo-X  6300,  (2)  X  6400- 
X  5800,  (3)  X  5900-X  5500,  (4)  X  56oo-X  5000.  For  regions  (i)  and 
(2),  one  was  a  Cramer  plate,  the  duplicate  a  Wratten  &  Wainwright 
plate.  No  plates  were  exact  duplicates,  as  the  slit-width  and  time  of 
exposure  were  varied.  One  85 -minute  exposure  was  made  on  a 
Hilger  spectroscope,  for  the  region  X  68oo-X  7700.  A  one-minute 
exposure  is  sufficient,  on  this  instrument,  for  the  shorter  wave- 
lengths. The  spectroscope  was  calibrated  with  the  argon  spectrum, 
and  the  readings  obtained  for  nitrogen  are  probably  correct  to  i  A. 
All  of  the  plates  obtained  with  the  large  grating  are  usable  save 
one  in  the  X  6300-X  6900  region  which  dried  very  unevenly. 
The  duplicate  plate,  however,  is  the  best  that  I  have,  and  the 
readings  obtained  from  it  are  believed  to  be  as  trustworthy  as 
those  in  any  portion  of  the  spectrum. 

The  work  that  has  thus  far  been  completed  is  as  follows: 

1 .  The  lines  in  the  immediate  vicinity  of  the  three  conspicuous 
" heads"  of  each  band  have  been  measured,  and  their  wave-lengths 
computed,  on  all  plates. 

2.  The  regions  X  55oo-X  5900   and  X  630O-X  6900   have  been 
completely  measured  and  computed. 

There  are  about  6400  lines  between  X  5000  and  X  6800,  and  274 
in  the  X  6623  band,  in  which  von  der  Helm  measured  119.  There 
appear  to  be  fully  as  many  in  all  the  other  bands,  although  in  most 
cases  the  number  actually  measured  is  much  less,  owing  to  the 
smaller  intensity  and  shorter  length  of  the  bands. 

The  measurements  were  made  on  a  55-cm  Geneva  dividing 
engine.  The  screw  was  carefully  calibrated  by  the  author  and  is 
believed  to  have  no  unknown  errors  greater  than  o .  002  mm.  In 
order  to  test  the  evenness  of  drying  of  the  plates,  the  international 
secondary  standards  were  first  corrected  for  non-normality  of  the 
dispersion  and  errors  of  the  screw,  and  were  then  fitted  as  nearly 
as  possible  to  a  linear  scale.  Only  standards  of  suitable  intensity 


POSITIVE  BAND  SPECTRUM  OF  NITROGEN  57 

were  used,  those  overexposed  being  evidently  untrustworthy.  In 
the  case  of  one  plate  in  the  X  63OO-X  6900  region,  the  average  devia- 
tion of  all  the  normals  from  a  linear  scale  was  less  than  o .  002  A. 
This  was  taken  to  indicate  that  the  screw  had  been  correctly  cali- 
brated. On  other  plates  there  was  a  general  drift  from  such  a  linear 
scale,  very  evidently  due  to  uneven  drying.  It  seldom  exceeded 
0.015  A  and  by  drawing  a  smooth  curve  through  the  plotted  read- 
ings of  the  normals,  the  correction  for  this  was  easily  made. 

When  the  wave-length  determinations  of  one  plate  were  com- 
pared with  those  of  a  duplicate  plate,  there  generally  appeared  a 
constant  difference  between  them.  This  difference  varied  from 
o.oi  A  to  0.04  A  on  different  sets  of  plates.  It  was  considered 
due  to  the  uneven  illumination  of  the  grating,  as  already  explained. 
Fortunately,  however,  we  have  interferometer  measurements  of 
the  three  mercury  lines  present  on  my  plates.  By  means  of  the 
ghosts  and  satellites  of  these  lines,  it  was  possible  to  determine  their 
position  with  great  accuracy,  in  spite  of  their  overexposure.  This 
settled  the  absolute  wave-lengths  from  \5ioo  to  \5goo.  One 
plate  in  each  of  the  other  two  regions  was  then  found  to  agree  per- 
fectly in  the  overlapping  portions.  I  thus  had  a  full  set  of  plates 
in  complete  agreement,  and  the  duplicate  plates  were  then  given  the 
proper  constant  correction  to  make  them  also  agree. 

The  values  of  the  wave-length  of  any  one  line,  as  determined  on 
different  plates,  then  seldom  differed  by  more  than  o .  01  A.  Several 
settings  were  made  on  each  line,  and  as  the  nitrogen  lines  are  fairly 
sharp,  the  average  experimental  error  of  setting  scarcely  exceeds 
0.003  A.  It  is  hoped,  therefore,  that  the  relative  error  of  all  save 
very  faint  or  hazy  lines  is  less  than  0.005  A,  and  that  the  abso- 
lute wave-lengths  are  in  general  correct  to  o.oi  A. 

Table  I  gives  the  wave-lengths  of  872  lines  forming  the  three 
principal  heads  of  the  bands.  The  lines  in  the  vicinity  of  all  the 
heads  given  by  von  der  Helm  were  measured,  although  in  several 
cases  there  is  no  real  head  present.  Several  other  heads  not  given 
by  von  der  Helm  were  noted  and  measured.  These  so-called 
"heads"  are  caused  by  the  proximity  of  several  heavy  lines,  accom- 
panied by  more  or  less  continuous  radiation.  The  measurements, 
in  all  cases,  cover  this  region  of  continuous  radiation,  which  is 
indicated  in  the  table  by  braces.  Frequently  the  haze  is  due 


58  RAYMOND  T.  BIRGE 

merely  to  the  scattering  of  light  in  the  photographic  film,  but  in 
most  cases  it  is  apparently  a  true  radiation. 

The  three  main  heads  of  a  band,  out  of  the  five  that  appear 
with  low  dispersion,  are  designated  I,  II,  and  IV.  The  bands 
themselves  are  designated  in  two  ways:  first,  by  the  division  into 
groups  (a  to/),  the  individual  bands  of  each  group,  from  red  to 
violet,  being  designated  by  Arabic  numerals;  the  second  method 
of  designation  is  that  proposed  by  Cuthbertson1  and  formulated 
mathematically  by  Deslandres.2  In  this  arrangement  the  position 
of  the  first  head  of  each  of  the  entire  set  of  57  bands  is  given  as  a 
function  of  two  independent  parameters,  p  and  n.  The  value  of 
these  parameters,  for  each  band,  is  given  immediately  below  the 
designation  of  the  band  according  to  the  first  arrangement.  The 
first  integer  refers  to  the  value  of  p,  the  second  to  n — the  values 
being  those  of  Deslandres.3 

The  three  columns  in  the  table  are: 

(i)  Intensity;  lines  marked  "  ?"  are  so  faint  as  to  preclude  an 
accurate  determination  of  wave-length;  (2)  wave-length — on  the 
International  System  (I. A.),  at  i5°C.,  760  mm;  (3)  character 
of  the  line.  In  this  regard  the  following  abbreviations  are  used: 

s.,        especially  sharp. 

b.,        broad. 

b.'d.,    broad,  probably  double. 

d.,        certainly  double. 

h.,        hazy. 

h.r.,     haze  on  the  red  side  (due  to  one  or  more  fainter  components  on  that 

side). 

h.v.,     haze  on  violet  side, 
n.s.,     a  non-symmetric  line  due  to  two  or  more  components  of  unequal 

intensity.     The  setting  was  made  on  the  center  of  gravity  of  the 

system. 

k.,        the  line  at  which  a  "head "  apparently  starts, 
a.,        argon. 

Von  der  Helm's  value  for  the  wave-length  in  air  for  the  general 
position  of  the  head,  together  with  the  frequency  in  vacuo,  is  given 
to  the  right  of  the  designation  of  the  head. 

*PhU.  Mag.  (6),  3,  348,  1902.  a  Comptes  rendus,  134,  747,  1902. 

3  See  Baly,  Spectroscopy,  p.  620,  1912  edition. 


POSITIVE  BAND  SPECTRUM  OF  NITROGEN 
TABLE  I 


59 


I 

2 

3 

i 

2 

3 

i 

2 

3 

/Id  4       /     6787.91 
U8-53     117,728.  i 

/IId5     /     6694-95 
\47-52     \  1  4,93  2.  6 

3 
4 

2 
2 
4 

4 

i 

3 

2 

66l3.l88 

.cs6i 
12.878 
•759 
•524 
.244 
.001 
11.722 
-603 

h.r. 

h. 
h. 

s. 

(i 

2 

I 
2 

6788.614 
•243 

.101 

87.970 

.834 

.712 

•  515 
.270 

k. 

f  4 

2 

I 
2 

3 

•      2 

I 
I 

(3 

13 

3 

6694.911 

•775 
•553 
•391 
.226 

93-774 
.610 

•474 
-367 
.242 
92.849 

k. 

/n.s. 
1  h.v. 

b. 

/IVd6    /     6594.425 
146-51     1  15,160.  i 

/lid  4     /     6778.35 
\48~53     Ii4,748.9 

1 

4 
6 

3 

2 

6594.418 
•175 
93  •  739 
-598 
•155 
92.568 

•423 
91.936 
.781 

k.b. 
h.v. 

i 
i 

{I 

2 

I 
I 
2 
2 

6779.972 
78.821 

.623 
.448 

77-949 
.538 
.288 
76.874 
.661 

k. 

/IVd5    /     6675.01 
\47-52     \  14,977-  2 

{I 

4 

2 

2 

3 

i 

(4 
14 

6674.908 
•  634 
-236 
.074 
73-8i7 
.615 
.446 

72-954 
-852 

k.b. 
b. 

/Id  7       /     6544-81 
145-50     115,275.2 

/IVd4   /     6758.98 

l48-$3       \  14,791  -2 

f/3 

\3 
i 

1   5 
4 

2 

6 

e 

4 
4 

6544.881 
•  .716 
.598 
•  432 
-237 
•095 
43  •  942 
•  714 
.616 
.460 
•251 

k. 
h. 

2 
2 

/I 
\I 
2 

I 

(i 

i 

4 

6759.243 
58.054 
57.807 
.665 

•355 
.067 
56.721 
.611 
•325 
55-948 

k. 

rid  6    /  6623.534 
146-51   115,093.6 

4 

2 

2 
'  4 

4 

2 

5 

I1 

b 

6623.574  - 

.417 
.281 
.  1  20 
22.915 

•795 
-658 

•395 
.130 
21.971 
-838 

k.b. 
b.h. 

b.h. 
n.s. 
s. 

/lid  7     /     6535.50 
\45-5o     115,296.8 

fid  5      /     6704.45 
\47-52     1  14,911.4 

6 
3 
4 
3 
4 
3 

4 

i 
4 

6535-655 
.  no 

34-924 
.627 
.482 
.188 
.028 

33-754 

•305 
.127 

s. 
d. 

h.r. 

/h.r. 
Ih.v. 

b. 

3 

2 
I 

3 
3 
3 
3 
3 
4 

6704.755 
•  634 
•514 
•363 
.132 
03.879 
.630 
.376 
.227 

k. 
h.d. 

/IId6     f     6614.023 
146-51     \  15,115.0 

6 

ft 

3 

6614.031 
13-789 
.678 

•5i4 

k. 
h. 

6o 


RAYMOND  T.  BIRGE 
TABLE  I— Continued 


I 

2 

3 

i 

2 

3 

i 

2 

3 

riv</7  J   6516.44 

\4S-5o     (15,341.6 

i 

{• 

5 

6441  .  134 
40.  768 
.563 
•392 
•150 
39.992 

•590 
.270 
.168 
38.887 

k.h.d. 

2 
? 
2 
I 

I 
2 
I 
2 

4 

6322.816 
.708 

•594 
.462 
-386 
.280 
.162 
.003 
21.797 

k.h. 

n.s. 
n.s. 

2 

4 

2 
2 
5 

6 

2 

6 
5 

65l6.6lO 
-403 
.256 
.166 
I5-897 

•759 
-586 
.407 
.181 
14.687 
•459 

h.r.k. 
h. 
h. 

riirf  10  r  6313.20 
(42-47   (15,835-5 

ri</9    r  6394.45 
143-48   (15,634.2 

| 

i: 

i 

4 

6314.420 
13-287 

-185 
.069 

12.957 
.720 
.626 
.214 
11.659 

k. 
h. 

h. 
h. 
h. 

.    fldB      r     6468.53 
\44-49     \  15,455  -3 

/2 

ij 

I 

5 

6394.628 
.442 
.284 
.122 
93-991 
.854 
.636 

k. 
h.v. 

! 

• 
, 

4 
4 

4 

2 

6 

2 

1 

[2 
2 

5 

6468  .  597 
.438 
.144 

67-951 
.802 

.634 
.416 
.280 
.142 
66.913 
.809 
.588 
•  442 

k.b. 

fh.r. 
\h.v. 

b. 

fllrfg     /     6384.93 
(43-48     (15,657.6 

rivd  10  r  6296.03 

\42-47       (15,878.8 

{: 

2 

3 
3 
•  4 
3 

2 
2 

4 

6386.096 
85.978 

•503 
.026 
84.900 
.627 

•451 
.322 
.O8l 
83-887 

k. 

d. 
b. 

b. 

3 

? 

3 
3 

6296.212 
.026 
95  805 
.606 

.077 

b.h. 
n.s. 

fiids    r   6459.04 

(44-49     (15,478.1 

ri  d  ii    r   6252.81 
141-46   (15,988.4 

6 

2 

5 

2 

3 

2 

3 

6459.673 
.181 
58.884 
.726    - 
•503 
•385 
.261 
.128 
57.810 
.669 
.460 
.086 

k. 
h. 

h.d. 

I 

2 

$ 

I 
I 

I 

6253.001 
52.806 
.670 
-587 
•494 
•377 
.226 

b.k. 

h. 
h. 

b. 

flV  dg    /     6367.55 
(43-48     115,700.3 

4 

2 

4 

2 

3 
3 
3 

6367.416 
.165 
66.808 
.252 
.107 
65-9I3 
.564 

h.r. 

{iid  ii  r  6243.51 

(41-46      \  l6,OI2.  2 

? 

2 
2 

I 

I 

6243.688 
•581 
.297 
42  .  944 
•  744 

s.h.v. 
h.r. 

rivds  r   6440.80 

\44-49     \i5,52i.8 

rid  10  r  6322.73 

\42-47     (15,811.6 

POSITIVE  BAND  SPECTRUM  OF  NITROGEN 
TABLE  I— Continued 


6l 


I 

2 

3 

I 

2 

3 

i 

2 

3 

I 

p 

3 

6242.601 
.402 
.199 

h. 

2 

I 
? 
'    ? 

I 

6I76.I26 

75-967 
.791 
.654 
•523 
•392 
.251 
.  112 

74-874 
.612 

k. 

3 

i 

2 

I 

6II9.454 
•312 
.129 
18.993 

b. 
b. 

riv  d  ii  /  6227.00 

(41-46       \  16,054.  7 

[IV  e  2    /     6102.60 
\48-52     \  16,382.0 

1 

I 

6227.096 
26.978 
.790 
.4l6 
.079 

h.k. 
b.h. 
h. 

h. 

| 

6lO2.736 
•514 
.381 
•259 

01-537 

k. 

flV  e  i  ? 
\49-S3 

/lei       /     6185.44 
\49~53     \  16,162.  6 

2 

I 
I 
? 

? 

I 

6161.648 
.276 

.131 
60.797 
.580 

-395 

b. 

{1^3        f     6069  .  60 
47-51     \  16,471.0 

? 

i 

2 

I 
I 

6l87.O22 

86.733 
.297 

85-874 
•570 

h.r. 
k. 
b.h. 

b. 

5 

(i 

2 

5 

i 

3 

2 

6069  .  663 

-463 
.280 

-174 
-034 
68  .  704 
-506 
.382 
.250 

b.k. 
h.v. 
h.v. 

fIVdl2     /       6160.43 

\40-45       \  16,228.  2 

fid  12 

Uo-45 

{I 

1 

6159.844 
.692 
•443 
.114 
58.952 
.581 
•433 
57.960 

h.k. 
h. 

h. 
h. 

d. 

{: 

i 
i 
i 
i 
i 
? 

6185.224 
.127 
84.937 
•  750 
•5i6 
•313 
.120 
.012 
83.861 

d. 
b. 
b. 
b. 

s. 

s. 

file  3     /     6062.44 
\47-5i     \  16,490.  5 

3 

2 
2 

6 
3 

6062  .  563 
.414 
.190 
61.984 
.500 

h.r. 
b. 
h.r. 

fie  2       /     6127.23 
\48-52     \  16,316.  i 

2 

I 
I 

4 
i 

2 

6127.374 
.208 
.087 
26  .  944 
•752 
•471 

h.v.k. 

fll  e  i  ? 
\49~53 

fIV«3    /     6045-55 
\47-5i     \  16,536.  6 

2 
2 
? 
? 
2 
? 

6178.549 
.170 
77-574 
•385 
•259 
76.809 

I 

I3 
13 

1   6 
i 

2 

4 

6045  .  484 
.407 

-173 
44.970 
.808 

•319 

k. 

h.r. 
d. 

/  h.r. 
\  h.v. 

fll  e  2      f     6119.  79 
(48-52     \  16,336.0 

2 
2 

g 

6120.602 

-273 
19.849 
.720 

h.v. 
k. 
h.v. 

file?  12    r   6175.32 

\40-45       \  16,189.  i 

f  I  e  4       f    6013  .  60 
\46-so     (16,624.4 

62 


RAYMOND  T.  BIRGE 
TABLE  I— Continued 


I 

2 

3 

i 

2 

3 

i 

2 

3 

\ 

3 
4 

6013.575 

•335 
•195 
.030 
12.907 
.772 
.567 

k.h.r. 

s. 

b. 

(IV  es    f     593595 
(45-49     \  1  6,84  1.  9 

F 

13 
6 

5882.615 

-479 
.320 

.016 

h. 
h. 

fh.v. 

(h.r. 

i 

3 

i 

3 
5 

5935-920 

-740 
.660 

•553 
.426 
.231 
.092 
34.925 
•  774 
.627 

k. 

h.r. 

fie  7       f     5854-69 
\43-47     1  1  7,075  -6 

file  4     f     6006  .  34 
(46-50     \  16,644.  5 

5 

2 
2 

7 
3 
4 

2 

/4 

\2 

5854  .  404 

•253 
.168 
.032 

53.873 
.666 
.462 
.286 
.168 

b.Ak. 

b. 
h.r. 

s. 

4 

2 

5 
4 
3 
4 

6006.477 

•341 
.118 
05.967 
-834 
.645 

b. 

f  I  e  6       f     5906  .  24 
\44-48     \  16,926.  6 

's 

i 

•  ? 
6 

2 

3 

2 
2 
3 

3 

5906.010 
05.900 
-792 
.672 
•503 
.368 
.285 
.126 
04  .  948 
.852 

b.k. 
h.v.b. 

s. 

jTVe4    f     5990.01 
\46-50     \  16,689.  9 

file  7     /     5847-67 
\43-47     117,096.1 

{' 
1 

4 

5989.812 
.636 
.519 
•  324 
.179 
88.702 

n.s.k. 

s. 

f  ? 
5 

I 

6 
i 
5 
4 

5847  .  740 
•5i8 
•  405 
.300 

•243 

.120 
.040 
46.815 
•578 

•  477 
.  in 

s.k. 

b.h. 
h.r. 
h.r. 
h. 

flic  6     f     589919 
\44-48     \  1  6,946.  7 

/I*  5       /     5959-25 
\45-49     116,776.0 

2 

5 

2 
2 

'3? 

I 

3 
3 

5899.070 
98.930 
631 
-523 
.401 
•  252 
.148 
.040 
97-874 

n.s.k. 
b. 
b. 

2 

5 
3 

5 

2 

3 

2 

3 

5959.220 
•053 
58.767 
.656 
.548 
-447 
•  342 
.206 

h.v.k. 
b. 

fIVe  7    /     5832.29 
143-47      117,141-2 

3 
6 

i 

3 
i 

f 

2 

4 

5832.054 
31.881 
•707 
•597 
•405 
•274 
.119 
30.941 
•839 

k. 
b. 

files     /    5952.02 
\45-49     \  16,796.  4 

fIVe  6    f     5883.49 
\44-48     \  1  6,  99  2.0 

4 
5 

{! 

2 
2 

5951-935 
.782 
.617 
.440 
•332 
•US 
.010 

h.k. 

I1 

b 

5883-517 
.446 
.146 
.029 
82.917 
.807 

k. 

fie  8       f     5804.28 
\42~46     \  1  7,  224.0 

POSITIVE  BAND  SPECTRUM  OF  NITROGEN 
TABLE  I— Continued 


I 

2 

3 

i 

2 

3 

x 

2 

3 

6 
i 

8 

3 
i 

6 

3 
3 

5804.135 
03.978 
.776 
•590 
.482 

.367 
•195 
.123 

02.980 
.858 

b.k. 
d. 

/lie  9     /     5748.18 
\4i-45     \  17,392.0 

{1 

5700.637 

.JI2 
5699  .  830 

5 

i 

(f 

I1 
fe 

2 
I 

8 

i 

[1 

5748.664 
.289 

.  IOI 

.008 

47.883 

.650 
.408 

.178 

.040 

46.939 

.615 
.487 

.250 
.149 

k. 

b. 
b. 

s. 

h.v. 
h. 

/IVeio/     5685.56 
Uo-44     117,583-7 

? 

i 
i 

5685.496 
.199 
.058 

b. 

JII  e  8     /     5797.23 
\42-46     (17,244.9 

/leu     /     5660.54 
l39~43     1  1  7,661.4 

5   • 

£ 

3 

5 

2 

2 
2 

5797-451 
-308 
.062 
96.969 
.830 
.707 
.6O2 

•513 
.412 
.299 

h.r. 
b. 

i 
? 

? 
i 

i 
i 

2 

5660.842 
•590 
.421 

•331 

.  240 

•115 

59-954 

k. 
b. 

/IV«9    /     5733-68 
\4i-45     \  1  7,436.0 

4 
4 
4 
i 

2      ' 

4 

i 

3 

i 

9 
i 

2 

5733-830 

-555 
-450 
-369 
.276 

•159 
32.992 
-830 

•  703 
.462 

-279 
31.921 

k. 

s. 
b. 

/He  ii   /     5653-31 
\39-43     117,683.9 

;iv«8  /  5782.23 

\42-46     \  17,289.  1 

? 
? 
? 
? 

5653  •  504 
.170 
52.676 
51.841 

s.h.r. 
s. 

5 
8 

i 
i 
5 
3 
3 
4 
6 
4 

5782.307 
•059 
81.943 
.849 
.740 
.566 
.426 

•239 
80  .  984 
•836 

b.k. 

/IVcn/     5639-17 
139-43     Ii7,728.2 

/I  e  10     f     5707-49 
\40-44     (17,516.0 

p 

p 
p 
? 

5639-349 
38.868 

37.899 

-775 

3 

2 
•  I 

2 
? 
p 

3 

5707-58o 
.462 
.301 

-131 
06  .  944 

.840 
•597 

k? 
h. 

b. 
h. 

A*  9       /     5755-20 
\4i-45     \  17,370.  8 

(I/  i 

149-52 

2 

4 

? 

3 
5 
5 
4 

i 
6 

2 

5755.415 
.188 
.074 

54.983 
.862 
.746 
.6l6 
.498 
.366 
•195 

h.k. 
h.v. 

Haze  5632.754  to  5632.361 
Very  faint  lines  to  5627  .  750 

J1I  e  10  /     5699.50 
\4o-44     \  17,540.  6 

rii/i    /   5622.97 
149-52   117,779-3 

3 

2 
? 

5701.358 
00.939 
-883 

? 

5622.610 

RAYMOND  T.  BIRGE 
TABLE  I— Continued 


I 

2 

3 

i 

2 

3 

i 

2 

3 

ri  e  12    r  5615.00 
138-42    117,804.5 

fIV/2 
\48-5I 

2 
2 

5 

2 
2 

6 
4 
3 

*5S53  996 
•924 
-730 
.600 
.491 
-362 
.204 
52.962 

b.h.k. 

b.h.v. 
b.h. 

i 
? 

? 

56I5-3I8 
.230 
.032 
14  .  QOO 

•779 
•695 
•573 
.387 
.230 

k. 

b. 
b. 

d. 

J 
(! 

2 

I 

3 
•  i 

2 
2 

5573-126 
72.894 

•737 
•551 
•347 
.247 

-039 
71.881 
.780 
.638 
.410 
•  320 

S. 

a. 
h.r.k. 

s. 
s. 

rn/3    r  5548.40 
147-50  1  18,018.2 

2 

3 
i 

i 
3 

2 
I 

5548.825 
.711 
.600 

•515 
-390 
.242 
•  137 

h. 

riie  12  r  5607.73 

\38-42     117,827.6 

i 
? 
? 
? 

5608.214 
.094 
07.687 
•375 

k. 

/I*  13     /     5570.6o 
\37-4i     117,946.5 

/IV/3    (5533-46 
\47-50     1  1  8,066.  9 

3 
i 

4 

2 
2 
2 

{1 

5570.777 
.679 
•501 
•354 
.201 
.013 
69.850 
.786 

k.h. 
b.h. 

d. 
h.v. 

ri/2     r  5592.57 

\48-5i     117,876.0 

5 

3 
i 
i 
i 
4 

? 
4 
i 

2 
2 

5533  504 
.406 
.238 
.164 
.041 
32-955 
.824 
.707 
599 
•473 
•349 
•251 
.146 

h.r. 

h.r. 
h. 

s. 
s. 
s. 

? 

3 

I 

{!. 

2 

I 

? 

? 

I 

5593-014 
92.881 

.657 
•514 
-364 
-283 

.130 
.013 
91.888 
.768 
-586 

h.v.k. 

h. 
h. 

file  13    f     5563.48 
\37-4i      117,969-4 

2 
I 

3 

i 
? 

? 
? 

? 

i 

5563  -  704 
•571 
•244 
.124 
.038 

62.937 
.828 
.696 
.612 
•405 

b.k. 
b.h. 

fII/2 

148-51 

ri«i4   r  5526.84 

136-40    \  1  8,088.  6 

2 

? 

I 

(l 

I 
2 
? 
2 
2 

5588.081 
87.989 
.883 
-742 
•531 
.440 
.190 
.064 
86.620 
.      -490 
•330 

k. 

b.n.s. 
h. 
h. 

2 

4 

5 
4 

2 

4 
4 
3 

5527-I50 
.027 
26.835 
.707 
.610 
.508 
•356 
.188 

k.h. 
s. 

JI/3       /     5553-63 
\47~50     \  18,001  .  2 

2 
2 

5554.258 
.130 

riie  14  r  5520.11 

136-40    \i8,no.6 

POSITIVE  BAND  SPECTRUM  OF  NITROGEN 
TABLE  I— Continued 


I 

2 

3 

i 

2 

3 

i 

2 

3 

/3 

H 

\i 

2 

5519.682 
•592 

•475 
.398 
.268 

fl«i5 

\35~39 

1 

/3 
\3 
3 

2 

3 

2 

I 

4 

5458.879 

•759 
.630 

•554 
•451 
•353 
•273 
•139 
.008 

57-903 
•797 
.697 

.587 

h.k. 

n.s. 
h. 
h. 

s. 
s. 

5 

2 

3 
5 

d 

3 
4 
3 

5484  .  730 

-593 

.488 

•338 
.225 
.094 
.018 
83-896 
.686 
-476 

b.k. 

h. 

s. 

71/4          /       5515-54 

\46-49     \  18,125.  6 

i 

8 

(I 

3 

2 

3 
3 

2 
2 

3 

55I5-758 
•594 
•451 
•239 
.178 
.081 
14-953 
•777 
.636 

•  496 
•325 
.190 

k.b. 

b. 
b.h. 

b. 
h.r. 
b.h. 

b.d. 
d. 

ri/6     /  5442.25 

\44-47     118,369.7 

JI/5       /     5478.73 
\45-48     \  18,247.  4 

2 
2 

/6 
14 
4 
4 
[1 

Is 

4 
3 
4 

5442.498 
.416 

•325 
.276 

.200 
.104 
41.981 
•932 
.833 
•751 
.640 

k. 

s. 

i 

d 

2 

'{i 

5478.575 
-471 
.266 
.124 
.007 
77.912 
.804 
.656 
.601 

n.s.k. 
b. 

rn/4   /  5510.55 

\46-49     \  18,142.  3 

4 

p 

p 

4 
4 

i 

5 

'  ? 
? 

i 

2 

<3 

2 

4 
3 

5511.096 
10.998 
.929 

•835 
.638 
.488 
.278 
.177 
.109 
.044 
09  .  936 
•847 
.736 
•545 
•  434 
•  316 

h.r. 

d.h.v. 
b. 
b. 

s. 
s. 

s. 

rn/6-  /  5437.03 

\44-47     118,387.3 

JH/5     /     5473-16 
\45-48     \  18,266.0 

5 

2 
2 
2 
•  2 
3 

3 
5 
3 

5437-328 
.197 
.027 

36.957 
.894 
.801 
.621 
•5l8 

•399 

k.d. 

s. 

b. 
b. 

s. 

{i 

(1 

5 
4 
5 

2 
I 
2 

5473-524 
.468 

•3i3 
.190 
.056 
72.936 
•590 
•  485 
•3i6 
.228 
•131 

k. 

h. 
h. 

h.v. 

JIV/4    /     5495-42 
\46-4Q     \  18,192.0 

i 
4 

2 

,    3 

1 

4 

5495-997 

•  885 

•763 
.692 

•593 
•  430 
•343 
•159 

a.(?) 

s. 
s. 
h. 
h. 
h.r. 

riv/6   r   5424-17 

\44-47     \8i,430-9 

• 

riv/s  /  5458.22 

\45-48     \  18,31  5.  9 

i 

2 
2 

5423-423 
•319 
.209 

66 


RAYMOND  T.  BIRGE 
TABLE  I— Continued 


I 

2 

3 

i 

2 

3 

i 

2 

3 

{: 

3 

2 

6 

4 
6 

i 

5423.014 
22.Q22 
.771 

.688 
•535 
•369 
.187 
•035 

b. 
b. 

i 

2 

5387.I92 
.050 

h. 

2 

? 

? 
? 

3 

5334.318 

.165 
.026 
33.878 
.762 

d. 
b.h. 

ri/s     r  5372.78 

142-45     1  18,607  .  2 

i! 

3 

5373-I89 
72.976 
.820 
.727 
.496 
•390 
.223 

h.k. 
b. 
b.h. 

riv/9  r  5323-40 

Ui-44    1  18,779.  8 

ri/7     r  5407.08 

\43-46     118,489.2 

i 
? 
? 
? 
? 
i 
? 

5323.821 

•523 
.411 
22.983 
.770 
•6l5 
.483 

b.h. 
b.h. 
n.s. 
b.h. 

2 

6 

i 
3 

I 

3 

2 

5407.575 
.411 
.129 
.049 
06.979 
.876 
.785 
•  730 
•590 
.528 

b.h. 
h.r.k. 

h.v. 

rii/s    r  5367.41 

\42-45     118,625.8, 

4 
3 
3 
3 
5 
'    3 

2 

3 

[  i 

i 

2 

5367.782 
-654 
.527 
.420 

.325 
.236 
.132 
.O8l 
66.973 

.853 
.760 

b. 
b. 

k. 

d. 

ri/io   r  5306.22 
140-43  118,840.0 

6 

2 
2 

I 
2 
I 
2 

5307.072 
.004 
06  .  859 

•529 
.146 
05.980 
.696 
.413 

k. 

rii/7    /  5401.83 
143-46   118,507.1 

4 
3  . 
4 
•4 
5 
3 

2 

,3 

i 

2 

6 

5401-943 
.810 
.689 
•565 
•  450 
•  340 
.189 

•US 
.024 
00.924 
•  654 

b. 
k. 
b. 

/iv/8  r  5353-73 

\42-45     118,673.4 

rn/io 

-Uo-43 

3 
3 
3 

i 
6 

2 

5354-073 

53  992 
.872 
.768 
.608 
•493 

k. 
b. 
n.s. 

2 

li 

i 

5302.604 
.170 
.6lO 
•524 
.885 

d. 

/iv/7  r  5387.82 
143-46    118,555.3 

ri/n    r  5274-35 

139-42     1  18,953.  9 

2 
2 

r  ? 
? 

{^ 

4 
4 

1 

3 

I  3 

5388.490 
•353 
.236 
.172 
.087 

.002 
87.856 
.767 
.604 
.518 

•447 
.385 
.283 

k. 

h. 
h. 

/I/  9       (     5339-27 
141-44     118,724.0 

i 
? 

2 

? 

5275.072 
74.891 

•777 
-347 

k. 
h.h.v. 

(I 

3 
i 
i 

? 

5339-432 
•393 
•294 
.192 
.089 
38.920 
• 

h-}k. 

d. 

ri/i2    r  5244-05 
138-41   119,063.9 

/n/9 

\4i-44 

{i 

5244.071 
43-782 

k. 

POSITIVE  BAND  SPECTRUM  OF  NITROGEN 
TABLE  I— Continued 


67 


I 

2 

3 

i 

2 

3 

i 

2 

3 

/I/  13   /  5213.04" 

137-40     \  19,177.  4 

i 

2 
I 
2 
2 
2 

5I96.O8O 

95.967 
.679 

•443 
.346 
94.854 

i 

5178.940 

/IV/I4 
\36-39 

{3 

i 

5213.808 
•540 
.021 

k. 

h.v. 

il 

i 
i 

2 

I 
I 
2 
2 

5I67.O6O 
66.992 
.872 
.766 
.676 
.410 

•309 
.l8l 
.058 

k. 

s. 

ri/i4   /  5183.84 

\36~39     119,285.4 

/II/I3    /     5207.79 
\37-4o     \  19,  196.  7 

1 

{: 

I 

(I 

5184-237 
83-970 
.843 
•734 
.679 
•550 
•445 
•394 

b.k. 
b. 

2 
2 

I 

3 

2 

I 

3 

i 

2 
2 

4 

5209.009 
08  .  669 
•503 
.300 

•157 
07.885 

•558 
.262 
06  .  894 
.800 
.024 

s. 
b.h. 

h. 

h.r. 
h. 

s. 

s. 

/!/  IS 
\35-38 

JII/I4 
\36~39 

e 

i 

5I55.323 
.2OI 

•095 

k. 

4 
3 

i 

2 

3 

2 

5179.876 

.567 
.460 
•  322 
.217 
.072 

n.s. 

AV/I3 
\37-40 

JI/i6 
\34~37 

(3? 

5196.370. 
.  196 

h.v. 

{'? 

5126.806 
.726 

k. 

The  following  table  (Table  II)  gives  the  measurements  of  all 
conspicuous  lines,  or  groups  of  lines,  in  the  bands  extending  from 
X  6800  to  X  7650,  as  taken  on  the  Hilger  spectroscope.  The 
probable  error  is  i  A. 

The  three  main  heads  are  designated  as  before,  using  only  the 
first  method  of  grouping.  The  columns  are:  (i)  wave-length  in 
air;  (2)  frequency  in  vacuo;  (3)  designation  of  head. 

Table  III  gives  Croze's  measurements  of  the  first  head  of  the 
bands  from  X  7600  to  X  9100.  The  probable  error  is  several 
angstroms. 

DISCUSSION 

The  discussion  naturally  falls  into  three  sections:  (i)  a  brief 
sketch  of  the  two  methods  previously  proposed  for  grouping  the 
heads  of  the  nitrogen  bands;  (2)  a  quantitative  test  of  the  com- 
parative validity  of  the  two  methods,  based  upon  the  data  given 


68 


RAYMOND  T.  BIRGE 
TABLE  II 


I 

2 

3 

i 

2 

3 

z 

2 

3 

7624.8 

13,111-5 

I«3 

7261.3 

13,768.1 

He  6 

7072.8 

14,134.8 

7613.5 
7589.4 

13,172.9 

He  3 
IV  c  3 

17254-3 
\725o.o 

13,789-4 

7059.6 

I4,l6l.2 

ric8 
\idi 

7505.6 

I  c  4 

7239.9 

13,808.5 

IV  c  6 

7048.5 

14,183.7 

lie  8 

7492  .  2 

13^343  -7 

He  4 

7233-1 

13,821.6 

7040.4 

I4,2OO.  2 

7469.6 

IV  c  4 

7228.5 

13,830.9 

7O28.  2 

14,224.7 

IV  c  8 

7445-3 

13,427.6 

7221  .6 

13,843.  7 

7016.5 

14,248.3 

7404.8 

13,501.0 

7214.0 

13,858.3 

7001.4 

14,279.1 

7386.1 

13,535-3 

I  c  5 

7205.2 

13,875-3 

6991.5 

14,299  3 

7375-6 

13,554-5 

lies 

7197-3 

13,890.5 

6978.6 

14,325.9 

{7366.8 

13,570.7 

7181.0 

13,921.8 

6968.0 

14,347.6 

Id2 

\7363.o 

13,577-7 

7165.0 

13,953  o 

lei 

6956.0 

14,372.3 

lid  2 

7352.8 

13,596.5 

IV  c  5 

7i53-o 

13,976.2 

He  7 

6946  .  o 

14,392.8 

7345-6 

13,609.9 

J  7U5  -2 

13,992.0 

6938.8 

14,408.1 

IV  d  2 

7338.3 

13,623.3 

17142.2 

13,997.5 

6929.5 

14,427.2 

13,637-0 

7132.2 

14,017.2 

IV  c  7 

6921.6 

14,443  8 

7323.4 

13,651-3 

7125.0 

14,031.4 

6906  .  o 

14,476.1 

73I5-3 

13,666.3 

7I2O.O 

14,041  .  2 

6896.6 

14,497.2 

7307.7 

13,680.6 

7II2.3 

14,056.5 

6875.5 

14,540.5 

I  d  3 

7291.2 

13,711.5 

7099  3 

14,082.0 

6865.2 

14,562.3 

Hd  3 

7274.0 

13,743-8 

Ic6 

7090.9 

14,098.7 

TABLE  III 


I 

2 

3 

i 

2 

3 

9101 

10,985 

b  i 

8043 

12,430 

1^7 

8903 
8707 

11,229 
11,482 

b  2 
b3 

7887 

12,676 

(168 
\Ic  i 

8541 

H,705 

64 

7742 

12,913 

II*a(?) 

8369 

11,946 

b$ 

7628 

13,106 

I<3 

8204 

12,186 

66 

in  the  preceding  tables;  (3)  a  summary  of  the  evidence  in  favor  of 
each  method,  based  upon  (a)  the  appearance  of  the  bands  under 
high  dispersion,  and  ordinary  conditions  of  excitation  (work  of  the 
author) ;  and  (b)  the  appearance  of  the  bands  under  low  dispersion, 
but  unusual  conditions  of  excitation  (work  of  previous  investigators) . 

SECTION  i 

The  nitrogen  lines  of  wave-length  longer  than  X  5100,  compris- 
ing the  First  Deslandres'  Group,  fall  into  57  similar  groups  of  lines, 
called  "  bands."  Each  band  contains  several  sets  (usually  five)  of 
particularly  heavy  and  close  lines.  These  sets  have  been  called 
the  " heads"  of  the  bands.  That  set  in  each  band  lying  farthest  to 


POSITIVE  BAND  SPECTRUM  OF  NITROGEN  69 

the  red  usually  ends  abruptly  on  the  red  side,  and  has  been  called 
head  I,  the  band  being  said  to  begin  at  this  point,  and  to  be 
degraded  toward  the  violet. 

In  an  ordinary  band,  such  as  is  found  in  the  Second  Deslandres' 
Group  of  the  nitrogen  spectrum  (X  5060  to  X  2814)  there  are  series 
of  lines  starting  at  the  head,  and  proceeding  with  diminishing 
intensity  toward  the  violet.  Near  the  head,  the  lines  of  such  a 
series  are  so  related  that  successive  frequency  intervals  form  an 
arithmetical  series.  This  is  Deslandres'  Law  for  band  series.  In 
the  First  Delandres'  Group,  however,  there  appear  to  be  no  rela- 
tionships between  the  250  or  more  lines  forming  each  "band." 
This  is  not,  therefore,  an  ordinary  band  spectrum. 

Relationships  first  appear  when  we  group  together  correspond- 
ing lines  in  successive  bands,  choosing  one  line  from  each  band. 
We  might  take  one  line  from  the  first  (I)  head  of  the  X  6623 
band,  another  from  the  first  head  of  the  X  6545  band,  etc.,  and 
thus  form  a  series.  Under  low  dispersion  the  set  of  lines  form- 
ing a  head  appears  as  a  single  broad  line.  Thus  successive  first 
heads  were  found  to  form  a  series  satisfying  Deslandres'  Law — • 
similarly  successive  second  (II)  heads,  etc.  Such  a  series  extends 
over  10  to  15  bands,  and  then  the  interval  between  successive  terms 
changes  abruptly.  Accordingly  the  ten  or  more  bands  represented 
in  such  a  series  have  been  classified  as  a  "group  of  bands."  The 
entire  First  Deslandres'  Group  is  composed  of  five,  and  possibly  six, 
such  subgroups,  which  we  have  designated  a  to/  respectively.  Von 
der  Helm  decided  that  this  was  the  best  method  for  grouping  the 
band  heads,  and  arranged  his  data  in  this  way.  I  shall  therefore 
refer  to  it  as  the  von  der  Helm  arrangement,  although  it  is  not 
original  with  him. 

The  second  arrangement  of  the  bands  was  first  suggested  by 
Cuthbertson.  In  this  the  head  of  a  band  in  one  of  the  above  groups 
is  related,  not  to  the  adjacent  band,  but  to  a  band  in  the  adjacent 
band  group.  In  the  series  thus  formed  we  have  only  as  many  terms 
as  we  have  band  groups,  and  the  spacing  between  terms  is  much 
greater  than  in  the  von  der  Helm  arrangement.  Since  a  series  con- 
tains the  head  of  only  one  band  of  a  group,  there  are  at  least  as 
many  series  as  there  are  bands  in  a  group.  It  is  possible  to  form 


yo  RAYMOND  T.  BIRGE 

n  such  series  having  at  least  three  terms  each,  and  6  more  having 
only  two  terms  each. 

The  reason  for  such  a  grouping  is  that  the  17  series  thus  formed 
are  identical  in  spacing  with  one  another,  and  also  with  the  five 
series  into  which  the  bands  of  the  Second  Deslandres'  Group 
have  been  divided.  Each  series  appeared  to  fulfil  Deslandres'  Law, 
and  is  known  as  Deslandres'  First  Progression.  Each  series,  more- 
over, is  displaced  relative  to  the  preceding  one  by  a  regularly  in- 
creasing amount.  Thus  the  corresponding  terms  of  the  several 
series  form  of  themselves  another  set  of  series,  also  approximately 
obeying  Deslandres'  Law,  and  known  as  Deslandres'  Second  Pro- 
gression. 

Thus  the  entire  set  of  the  first  heads  of  the  bands  in  the  First 
Deslandres'  Group  can  be  jepresented  as  a  function  of  two  param- 
eters, p  and  n.  The  variation  of  n  gives  the  First  Progression, 
that  of  p  the  Second.  Deslandres  considered  that  both  progressions 
obeyed  his  law,  and  wrote  the  complete  formula 

v=A+B(n+Cl)*+C(p+c3y.  (i) 

In  this  formula  we  can  make  a  linear  transformation  of  variables 


and  obtain/  (k,  /),  also  of  second  degree  in  each  parameter,  and  so 
giving  the  ordinary  Deslandres'  Law  when  one  parameter  alone  is 
varied.  In  such  a/  (k,  I)  successive  integral  values  of  k  (I  remain- 
ing constant)  give  the  heads  of  the  successive  bands  of  one  group 
of  the  von  der  Helm  arrangement.  On  the  other  hand,  /  has 
different  values  for  successive  band  groups. 

Fig.  i  may  make  this  clearer.  This  figure  gives  the  general 
position  of  the  first  head  of  every  band,  plotted  with  frequency  as 
one  co-ordinate  and  the  value  of  p  as  the  other.  Any  horizontal 
succession  of  heads,  for  which  p=  constant,  gives  Deslandres'  First 
Progression.  The  value  of  n  for  each  head  is  plotted  beside  it,  and 
any  succession  of  heads  for  which  n=  constant  gives  the  Second 
Progression.  The  series  /=  constant  indicates  one  of  the  band 
groups  of  the  von  der  Helm  arrangement. 


POSITIVE  BAND  SPECTRUM  OF  NITROGEN 


-3 


\    \ 


+' 


M  O  O\  00 

M  V)  ^  ^ 


M  O 

^t  ^f 


O  00  t^,  vO  io  •* 

fO  CO  fO  PO  ro  «O 


72  RAYMOND  T.  BIRGE 

SECTION   II 

That  portion  of  the  nitrogen  spectrum  under  investigation 
appears  to  be  formed  of  two  superimposed  spectra.  One  of  these 
consists  of  lines  of  regular  arrangement,  the  other  of  lines  arranged 
irregularly.  A  graph  of  the  lines  of  several  bands  of  the  e  group 
indicates  that  perhaps  50  out  of  the  250  lines  of  each  band  belong 
to  the  regular  spectrum.  These  sets  of  50  lines  have  a  similar 
appearance  in  each  band.  It  is  thus  possible  to  identify  correspond- 
ing lines  in  successive  bands  and  to  form  them  into  series  extending 
through  one  band  group,  and  obeying  Deslandres'  Law  as  a  first 
approximation.  I  shall  call  each  of  the  50  series  thus  formed  a 
" simple"  series. 

The  first  heads  of  successive  bands  are  composed  mainly  of 
several  such  series,  and  the  general  position  of  the  first  heads  of 
successive  bands,  under  low  dispersion,  forms  roughly  such  a  series. 
Table  IV  gives  the  simple  series  of  longest  wave-length  in  each 
band  group.  It  is  therefore  composed  of  the  " first"  heavy  line 
in  each  band,  in  the  case  of  all  the  bands  photographed  under  high 
dispersion.  For  the  others  the  approximate  position  of  the  edge 
of  the  first  head  is  used,  as  given  in  Tables  II  and  III.  Deslandres' 
Law  demands  that  the  first  frequency  differences,  given  in  the  fifth 
column,  shall  form  an  arithmetical  progression,  the  second  differ- 
ences (sixth  column)  being  a  constant.  The  probable  experimental 
error,  in  terms  of  frequency,  varies  from  o .  04  at  X  5000  to  o .  02  at 
\68oo.  Such  an  average  error  in  the  measurements,  however, 
may  cause  an  average  variation  four  times  as  large  in  the  second 
differences  given  in  the  last  column. 

Each  series  evidently  obeys  Deslandres'  Law  for  the  major 
portion  of  its  extent,  but  deviates  from  this  law  near  the  violet 
end  of  the  group.  This  is  true  for  series  in  all  band  spectra,  Des- 
landres' Law  holding  only  near  the  head  of  a  series.  The  only 
formula  holding  for  an  entire  series  is  that  of  Thiele.1  It  contains 
eight  undetermined  coefficients  and  so  is  very  difficult  to  work  with. 
I  have  preferred  to  use  simply  Deslandres'  Law,  or  a  slight  modifica- 
tion of  it,  and  to  note  whether  there  was  a  regular  deviation  from 
this  law. 

1  Astrophysical  Journal,  6,  65,  1897. 


POSITIVE  BAND  SPECTRUM  OF  NITROGEN 
TABLE  IV 


73 


DESIGNATION 

\ 

FREQUENCY 

FIRST 

SECOND 

>    » 

(AiR) 

(vacua) 

DIFFERENCE 

DIFFERENCE 

/    16 

34-37 

5126.81 

19,499.86 

107.88 

/    15 

35-38 

5I55-32 

19,391.98 

0.27 

108.15 

/    14 

36-39 

5184-24 

19,283.83 

I  .  22 

109.37 

/    13 

37-40 

5213-81 

19,174.46 

1.27 

110.64 

/    12 

38-41 

5244.07 

19,063.82 

i-39 

112.03 

/    ii 

39-42 

5275-07 

18,951.79 

i-49 

H3-52 

/    10 

40-43 

5306.86 

18,838.27 

1.32 

114.84 

/      9 

41-44 

5339-41 

18,723.43 

i  .58 

116.42 

/      8 

42-45 

5372.82 

18,607.01 

1.65 

118.07 

/      7 

43-46 

5407  •  13 

18,488.94 

1.50 

H9-57 

/      6 

44-47 

5442.32 

18,369.37 

1.62 

121  .  19 

/      5 

45-48 

5478.47 

18,248.18 

1-63 

122.82 

/      4 

46-49 

55T5-59 

18,125.36 

i  .64 

124.46 

/      3 

47-50 

5553-73 

18,000.90 

i-55 

126.01 

/      2 

48-51 

5592-88 

17,874.89 

0.52 

126.53 

/      i 

49-52 

5632-75 

17,748.36 

e    15 

35-39 

5484.34 

18,228.65 

141.19 

e    14 

36-40 

5527-I5 

18,087.46 

0.46 

I4I-65 

e    13 

37-41 

5570.78 

17,945.81 

0.69 

142.34 

e    12 

38-42 

5615-32 

17,803.47 

0.83 

143-17 

e    ii 

39-43 

5660  .  84 

17,660.30 

1.07 

144.24 

e    10 

40-44 

5707.46 

17,516.06 

1.02 

145.26 

e      9 

41-45 

5755-19 

17,370.80 

1.23 

146.49 

e      8 

42-46 

5804.13 

17,224.31 

1.40 

147.89 

e      7 

43-47 

5854-40 

17,076.42 

1.32 

149.21 

e      6 

44-48 

5906.01 

16,927.  21 

I  .46 

150.67 

74 


RAYMOND  T.  BIRGE 
TABLE  IV— Continued 


DESIGNATION 

A 

FREQUENCY 

FIRST 

SECOND 

(Am) 

(vacuo) 

DIFFERENCE 

DIFFERENCE 

P    n 

e      5 

45-49 

5959-05 

16,776.54 

i-43 

152.10 

e      4 

46-50 

6013.57 

16,624.44 

1-52 

153  62 

«      3 

47-$I 

6069.66 

16,470.82 

«•$! 

155   *3 

tf        2 

48-52 

6127.37 

16,315.69 

1.41 

156.54 

«         I 

49-53 

6186.73 

16,159.15 

<*     12 

40-45 

6185.22 

16,163.09 

175.18 

d     II 

41-46 

6253.00 

15,987.91 

i-35 

176.53 

d    10 

42-47 

6322.82 

15,811.38 

1.03 

I77-56 

<*     9 

43-48 

6394-63 

15,633  82 

I.  21 

178.77 

d     8 

44-49 

6468  .  60 

15,455  05 

1-36 

180.13 

<*      7 

45-50 

6544-88 

15,274.92 

i  34 

181.47 

d     6 

46-51 

6623.57 

l5,093-45 

1.28 

182.75 

<*     5 

47-52 

6704.75 

14,910.70 

i-43 

184.18 

<*     4 

48-53 

6788.61 

14,726.52 

1.8 

186.0 

rf     3 

49-54 

6875-5 

14,540.5 

192.9 

d        2 

50-55 

6968.0 

14,347-6 

186.4 

d     i 

51-56 

7059.6 

14,161.2 

c      8 

43-49 

7059  .  6 

14,161.2 

208.2 

'      7 

44-50 

7165.0 

13,953-0 

209.2 

c      6 

45-51 

7274.0 

13,743  8 

208.5 

«      5 

46-52 

7386.1 

13,535-3 

215-4 

c      4 

47-53 

7505-6 

i3,3i9-9 

208.4 

c      3 

48-54 

7624.8 

i3,iii-5 

198.5  (?) 

C        2 

49-55 

7742-     (?) 

12,913-    (?) 

237-    (?) 

C         I 

50-56 

7887. 

12,676 

6      8 

43-50 

7887 

12,676 

246 

POSITIVE  BAND  SPECTRUM.  OF  NITROGEN 
TABLE  TV— Continued 


75 


DESIGNATION 

A. 

(AIR) 

FREQUENCY 

(vacua) 

FIRST 
DIFFERENCE 

SECOND 
DIFFERENCE 

p    n 

b      7 

44-5  1 

8043 

12,430 

244 

b      6 

45-52 

8204 

12,186 

240 

b      5 

46-53 

8369 

11,946 

241 

b      4 

47-54 

8541 

11,705 

223 

b      3 

48-55 

8707 

11,482 

253 

b         2 

49-56 

8903 

11,229 

244 

b      i 

50-57 

9101 

10,985 

In  groups  d  and  e  it  is  occasionally  doubtful  what  line  forms  the 
beginning  of  a  new  band.  In  the  first  heads  of  the/  group,  however, 
there  appears  an  extremely  heavy  doublet,  the  successive  pairs 
of  lines  having  not  only  the  same  relative  intensity,  but  also  a  con- 
stant frequency  difference.  The  doublets  thus  form  two  simple 
series,  of  which  that  of  longer  wave-length  has  been  used  for  the  / 
group  of  Table  IV.  In  /  i  only  one  member  of  the  doublet  is 
present— that  of  shorter  wave-length.  Hence  it  does  not  fit  well 
with  the  other  lines  in  Table  IV.  I  give  in  Table  V  the  simple 
series  formed  from  the  more  refrangible  member  of  the  doublet. 

The  first  nine  terms  of  this  series  can  be  fitted  into  the  ordinary 
Deslandres'  formula 

v=A+B(m+c)2  (2) 

with  an  average  difference  between  observed  and  computed  values 
of  0.005  A.  For  the  less  refrangible  member  of  the  doublet  the 
corresponding  average  difference  is  0.006  A,  and  the  constants  for 
this  latter  series  are: 

^4  =  22,900.627 

B=—      0.8000 
c=  +      0.260 

w  =  8o  to  72 

The  beginning  of  the  deviation  from  Deslandres'  Law  occurs, 
in  both  series,  at  a  point  of  minimum  intensity  at/  10  (X  5306). 


76 


RAYMOND  T.  BIRGE 
TABLE  V 


DESIGNATION 

A 

(Are) 

FREQUENCY 

(vacua] 

FIRST 
DIFFERENCE 

SECOND 
DIFFERENCE 

P   » 

/      I 

49-52 

5632.754 

17,748.361 

127.701 

/        2 

48-51 

5592.514 

17,876.062 

1.669 

126.032 

/      3 

47-50 

5553-362 

18,002.094 

I  597 

124-435 

/      4 

46-49 

55I5.239 

18,126.529 

1.629 

122.806 

/      5 

45-48 

5478.124 

18,249.335 

1.607 

121.199 

/      6 

44-47 

5441.981 

18,370.534 

1.615 

119.584 

/      7 

43-46 

5406.785 

18,490.118 

I-57I 

118.013 

/      8 

42-45 

5372.496 

18,608.131 

1.584 

116.429 

/      9 

41-44 

5339  089 

18,724.560 

1-544 

114.885 

/    10 

40-43 

5306.529 

18,839.445 

1-479 

113.406 

/    IT 

39-42 

5274-777 

18,952.851 

1-379 

112.027 

/    12 

38-41 

5243-782 

19,064.878 

1.448 

110.579 

/    13 

37-40 

5213-540 

I9,I75.457 

1.  197 

109.382 

/    14 

36-39 

5183  970 

19,284.839 

1-364 

108.018 

/  is 

35-38 

5155.095 

19,392.857 

At  this  same  point  the  frequency  difference  of  the  doublet  also 
begins  to  diminish.  For  these  two  reasons  it  appears  that  the  / 
group  consists  really  of  two  groups,  having  a  point  of  coincidence 
at  X  5306.  Table  VI  gives  the  frequency  difference  of  the  doublets 
for  the  en  tire /group. 

I  have  thus  far  been  unable  to  find  any  other  strong  series 
lying  within  the  heads  of  the  /  group.  In  the  d  and  e  groups, 
however,  there  are  at  least  15  series,  distributed  among  the  three 
heads.  In  most  of  these  the  second  difference  remains  approxi- 
mately constant  for  six  or  eight  terms;  in  a  few  it  forms  more 
nearly  an  arithmetical  progression,  the  third  difference  being  con- 
stant. Such  a  relation  can  be  satisfied  by  adding  one  more  term  to 
Deslandres'  Law,  so  that  it  reads: 

v  =  A  +B(m+c)2+C(m+c)s .  (3) 


POSITIVE  BAND  SPECTRUM  OF  NITROGEN 
TABLE  VI 


77 


DESIGNATION 

ft 

ft 

/4 

/a 

/6 

/7 

i» 

Difference  (  in  —  ) 

I-I73 

I-I93 

I  .  167 

1-157 

i  .  161 

1  .176 

1.123 

\       A  / 

DESIGNATION 

/9 

/io 

/" 

/« 

/I3 

/I4 

/IS 

Difference  '  

I.I27 

i.:75 

I  .064 

1-059 

1-034 

I  .OC»6 

0.876 

In  the  fifteen  series  the  average  difference  of  experimental  and 
calculated  values  is  slightly  more  than  o.oi  A.  In  some  cases  it 
is  over  0.02  A  and  evidently  exceeds  the  experimental  error  of 
measurement.  The  lines  forming  the  doublets  in/  are  very  difficult 
to  measure  correctly,  because  of  their  great  intensity,  and  the 
nearness  of  adjacent  lines.  Yet  they  fit  into  series  better  than  any 
other  set  of  lines.  Hence  the  deviations  from  formulae  (3)  or  (2), 
in  the  case  of  other  series  are  real,  and  not  due  to  experimental 
errors. 

The  spacing  arrangement  in  different  series  varies  slightly,  so 
that  series  often  tend  to  cross  one  another,  and  this  gives  successive 
heads  an  entirely  different  appearance.  This  can  best  be  shown  by 
the  five  series  in  heads  IV  d.  These  five  series  include  nearly  two- 
thirds  of  all  the  lines  present  in  these  heads,  and,  with  two  excep- 
tions, every  strong  line.  Series  5  and  e  start  from  the  same  line 
and  gradually  diverge.  Series  6,  at  the  fifth  term,  breaks  into  a 
doublet,  the  components  of  which  in  turn  diverge.  The  middle 
of  the  doublet  is  used  for  the  last  two  terms.  Such  a  sudden 
splitting  of  a  line  into  a  doublet  is  common  in  the  series  found  in 
band  spectra,  and  there  are  numerous  examples  of  it  in  the  spectrum 
under  investigation.  The  five  series  are  given  in  Table  VII. 

The  foregoing  portion  of  Section  II  has  been  concerned  simply 
with  the  law  followed  by  individual  simple  series,  each  being 
considered  entirely  independently.  There  are  also  -relationships 


RAYMOND  T.  BIRGE 


TABLE  VII 

IV  d  a 


(Air) 

Frequency 
(vacua) 

First 
Difference 

Second 
Difference 

6758.054 

14,793.111 

184.265 

6674  .  908 

14,977.376 

1.460 

182.805 

6594.418 

15,160.  181 

I-3I2 

181.493 

6516.403 

15,341.674 

1-340 

180.153 

6440  .  768 

15,521.827 

1-349 

178.804 

6367.416 

15,700.631 

1.251 

177-553 

6296.  212 

15,878.184 

1.020 

176.533 

6226.978 

16,054.717 

I  .  165 

175  368 

6159.692 

16,230.085 

IV  d  ft 


6757.355 

14,794.642 

184.242 

6674.236 

14,978-884 

1-383 

182.859 

6593  739 

15,161.743 

1.411 

181.448 

65I5-759 

i5,343-i9i 

1.322 

180.126 

6440.150 

I5,523-3I7 

1.311 

178.815 

6366.808 

15,702.132 

1-234 

177-581 

6295.606 

15,879-713 

1.127 

176.454 

6226.416 

16,056.167 

I.  012 

175-442 

6159.114 

16,231  .609 

IV  d  7 


6756.666 

14,796.151 

184.127 

6673.615 

14,980.278 

1.320 

182.807 

6593  -155 

15,163.085 

1.340 

181.467 

6515.181 

15,344.552 

1.352 

180.115 

6439  590 

15,524.667 

1.272 

178.843 

6366.252  • 

15,703.510 

1.306 

177.537 

6295.077 

15,881.047 

POSITIVE  BAND  SPECTRUM  OF  NITROGEN 


79 


TABLE  VII— Continued 
IV  d  8 


A 

(Air) 

Frequency 

(vacua) 

First 
Difference 

Second 
Difference 

6755.948 

I4,797-724 

184.040 

6672.954 

14,981  .  764 

1-368 

182.672 

6592.568 

15,164.436 

1-393 

181.279 

6514.687 

15,345.715 

1-435 

179.844 

6439.220 

l5,525-559 

1.304 

178.540 

6366.010 

15,704.099 

IV  d  e 


6755-948 

14,797.724 

184.268 

6672.852 

14,981.992 

1.491 

182.777 

6592.423 

15,164.769 

1.293 

181.484 

6514.459 

15,346.253 

1-374 

180.110 

6438.887 

15,526.363 

1.273 

178.837 

6365  .  564 

15,705.200 

between  the  spacing  arrangement  of  simple  series  in  different  band 
groups.  This  can  best  be  studied  from  the  standpoint  of  the  Cuth- 
bertson  arrangement. 

In  a  two-parameter  formula  such  as  (i)  there  may  be  included 
one  line  from  each  band  in  the  entire  spectrum.  It  therefore  com- 
prises several  simple  series.  The  entire  set  of  simple  series,  one  for 
each  band  group,  satisfying  separately  and  collectively  such  a  two- 
parameter  formula  I  call  a  " complete"  series.  When  the  lines  of 
any  complete  series  are  regrouped  to  form  the  p  and  n  progressions , 
it  appears  that  formula  (i)  is  not  the  correct  functional  form. 
Table  VIII  shows  this  clearly.  In  this  table  I  give  only  the  average 
frequency  intervals  of  the  two  progressions,  using  the  data  given 
in  Table  IV. 


8o 


RAYMOND  T.  BIRGE 
TABLE  VIII 


FIRST  PROGRESSION 

SECOND  PROGRESSION 

p  =  CONST  ANT 

n  =  CONST  ANT 

First 

Second 

First 

Second 

n 

Frequency 
Difference 

Frequency 
Difference 

P 

Frequency 
Difference 

Frequency 
Difference 

54 

49 

1615.0 

1432.3 

53 

25-6 

48 

27-3 

1589-4 

1405.0 

52 

29.9 

47 

28.0 

1559-5 

1377  0 

5i 

28.9 

46 

27-8 

1530  -6 

1349   2 

50 

29.0 

45 

27.8 

1501.6 

1321.4 

49 

29.6 

44 

28.0 

1472.0 

1  293   4 

48 

29.6 

43 

28.6 

1442.4 

.   1264.8 

47 

29.7 

42 

28.5 

1412.7 

1236.3 

46 

29.9 

4i 

28.9 

1382.8 

1207.4 

45 

30.2 

40 

29.4 

1352.6 

1178.0 

44 

30  3 

39 

29-7 

1322.3 

1148.3 

43 

30.8 

38 

30-3 

1291.5 

1118.0 

42 

31.2 

37 

31.0 

1260.3 

1087.0 

4i 

31-6 

36 

31.0 

1228.7 

1056.0 

40 

32-4 

35 

33  4 

1196.3 

IO22.6 

39 

3i-3 

34 

1165.0 

38 

34-5 

"30.5 

37 

The  second  difference  is  an  approximate  arithmetical  progression 
and  requires  a  function  of  the  type  given  in  formula  (3).  Instead 
of  formula  (i)  we  must  therefore  use: 

v=A+B(n+ciy+r(n+cl)*+C(p+c2)*+s(p+c2)* .  (4) 

Since  the  variation  of  both  n  and  p  has  the  same  functional  form, 
it  follows  that  the  variation  of  both  together,  such  as  we  find  in  a 
simple  series,  has  also  this  same  form.  For  that  reason  it  is  possible 
to  combine  two  simple  series  in  order  to  determine  the  constants  of  a 
complete  series.  The  two  conditions  imposed  upon  such  a  pair  of 


POSITIVE  BAND  SPECTRUM  OF  NITROGEN  81 

simple  series  are:    (i)  each  simple  series  must  fit  formula  (3);    (2) 
both  simple  series  must  have  the  same  third  difference. 

In  formula  (3)  this  third  difference  equals  6C;  in  (4)  it  is  6(r+s). 
It  is  therefore  the  same  for  both  simple  series.  When  the  constants 
of  a  complete  series  are  thus  determined,  all  other  simple  series  in- 
cluded in  the  complete  series  have  definite  predicted  positions. 

If  we  now  choose  the  simple  series  given  in  Table  IV,  using  only 
the  band  groups  for  which  we  have  accurate  measurements  (groups 
/,  e,  and  part  of  d),  it  appears  that  all  three  simple  series  satisfy 
condition  (i),  but  no  two  of  them  satisfy  condition  (2).  It  is 
therefore  impossible  to  group  them  together  into  a  complete  series 
satisfying  formula  (4) ,  and  so  the  first  lines  of  the  first  heads  of  all 
bands  do  not  satisfy  the  Cuthbertson  arrangement.  Another  way 
of  stating  this  is  that  -the  several  First  Progressions  are  not  identical 
with  one  another.  This  was  evident  in  compiling  Table  VIII. 
There  are  eight  intervals  in  this  table  whose  values  can  each  be 
derived  from  two  different  First  Progressions  (and  similarly  for 
the  Second  Progressions) ,  using  only  accurate  data.  For  these  eight 
intervals  the  average  difference  of  the  two  values  is  0.2  A,  more 
than  ten  times  the  experimental  error. 

In  the  I  heads  of  the  d  group  there  are  three  heavy  lines  in  all. 
The  two  of  shorter  wave-length  form  a  doublet  of  the  same  con- 
stant frequency  difference  as  that  in  the  /  group.  This  suggested 
the  combination  of  these  two  series  of  doublets  into  two  com- 
plete series,  which  should  differ  from  one  another  only  by  a  con- 
stant value.  It  appears  that  the  two  simple  series  formed  from 
the  doublets  in  the  d  group  are  compatible  with  those  of  the  / 
group,  and  so  this  rearrangement  into  complete  series  is  possible. 

The  simple  series  in  the  d  group,  of  shorter  wave-length,  is 
given  in  Table  IX. 

Using  the  two  simple  series  given  in  Tables  V  and  IX,  we  get 
the  following  constants  for  the  complete  series.  The  derivation  is 
rather  laborious,  and  the  computations  were  not  made  by  a  strictly 
least-squares  method : 

A  =22,108.476  r  =+0.0245 

B=—    18.0562  s=—   .0254 

C  =  +    17-2474  *  =  +   .3365 

Ca=-\-     .7222 


82 


RAYMOND  T.  BIRGE 


For  p  and  n  the  derived  values  are  respectively  three  and  four 
units  lower  than  Deslandres'  values,  which  I  have  consistently 
used  in  designating  the  bands.  This  shows  not  only  that  the  values 
of  cr  and  c2  (which  define  the  " phase"  of  a  series)  are  meaningless 
without  more  accurate  data,  but  also  that  no  deductions  can  be 
drawn  from  the  exact  value  of  p— n  for  any  band  group. 

TABLE  IX 


DESIGNATION 

A 

FREQUENCY 

FIRST 

SECOND 

(AIR) 

(vacua) 

DIFFERENCE 

DIFFERENCE 

P    » 

d      4 

48-53 

6787.712 

14,728.479 

184.174 

d     5 

47-52 

6703.879 

14,912.653 

1  .  291 

182.883 

d     6 

46-51 

6622.658 

15,095   536 

1.306 

181.577 

d     7 

45-50 

6543.942 

15,277.113 

1-335 

180.242 

d     8 

44-49 

6467  .  634 

15,457-355 

i  352 

1  78  .  890 

d     9 

43-48 

6393.636 

15,636.245 

I  .  2IO 

177.680 

d   10 

42-47 

6321.797 

15,813.925 

For  eight  terms  from  the  /  group,  and  seven  from  the  d  group, 
the  average  difference  (obs.  — calc.)  is  0.005  A.  For  the  less  re- 
frangible member  of  the  doublet  we  have 

4  =  22,107.315 

The  other  constants  remain  the  same.     For  14  terms  the  average 
difference  (obs.  — calc.)  is  o.oi  A. 

By  means  of  the  constants  given  above  we  can  obtain  the 
theoretical  position  of  corresponding  simple  series  in  all  other 
band  groups.  From  the  position  of  the  component  simple  series, 
in  the  heads  of  the  d  and  /  groups,  we  snould  expect  the  predicted 
series  in  the  b  and  c  groups  to  lie  just  to  the  violet  of  the  rough 
measurements  of  the  first  heads  in  those  groups.  This  is  found 
to  be  the  case,  within  the  limits  of  experimental  error.  In  the  e 
group,  however,  where  we  have  accurate  data,  there  is  no  series 
in  the  predicted  position.  All  series  in  I  e  have  a  slightly  different 
spacing  arrangement,  and  one  of  them  gradually  crosses  the  pre- 
dicted series. 


POSITIVE  BAND  SPECTRUM  OF  NITROGEN  83 

Thus  the  only  Cuthbertson  arrangement  I  have  been  able  to 
get  is  between  alternate  rather  than  adjacent  groups.  As  already 
pointed  out,  k  \  —  ^(p~\-n)\  and  /  {  =%(p—n)\  are  the  parameters 
in  the  von  der  Helm  arrangement,  corresponding  to  p  and  n  in  the 
Cuthbertson  arrangement.  In  this  latter  arrangement  the  first 
heads  of  all  the  bands  are  represented  by  integral  values  of  p  and  n. 
In  the  von  der  Helm  arrangement  integral  values  of  k  give  a  simple 
series.  If,  however,  we  keep  k  constant,  and  give  /  successive 
integral  values,  we  get  corresponding  first  heads  only  in  every 
alternate  band  group.  (See  series  k  =  constant  on  Fig.  i.)  For 
the  intermediate  groups  /  has  the  value  of  an  integer  plus  one-half, 
and  cannot  be  satisfied  by  integral  values  of  p  and  n.  Therefore 
we  might  expect  to  find  related  simple  series  only  in  every  alternate 
group.  I  have  at  present  no  other  numerical  evidence  either  for 
or  against  this  view. 

The  previous  discussion  shows  that  many  more  lines  can  be 
fitted  into  series  on  the  von  der  Helm  arrangement  than  on  the 
Cuthbertson.  This  naturally  follows  from  the  fact  that  each 
simple  series  involves  only  one  parameter,  while  the  Cuthbertson 
arrangement  involves  two.  The  individual  series  in  different  band 
groups  should  have  related  spacing  arrangements,  given  implicitly 
by  formula  (4).  The  data  show,  however,  that  the  relation  is  in 
general  not  accurate  within  the  limits  of  experimental  error. 

One  further  point  of  interest  is  the  continuity  of  successive 
band  groups.  The  heads  of  the  last  band  of  one  group  practically 
coincide  with  those  of  the  first  band  of  the  succeeding  group.  In 
this  connection  the  band  at  X  6186  is  the  most  interesting  in  the 
entire  spectrum.  In  this  band  we  have  at  6186.7  a  head  which 
agrees  in  its  general  position  and  appearance  with  the  designation 
I  e  i ;  similarly  at  6185 . 2  a  head  Id  12.  The  entire  appearance  of 
the  band  is  that  of  a  d  band,  and  it  is  doubtful  whether  the  e  group 
is  represented  save  by  I  e  i,  although  I  have  recorded  in  Table  I 
the  lines  in  the  vicinity  of  the  theoretical  position  of  II  e  i  and 
IV  e  i. 

In  the  case  of  the  e  and  /  groups,  the  theoretical  position  of 
I  e  1 6  is  5443.3,  almost  coinciding  with  the  strong  1/6  head  at 
5442.3.  Deslandres  records  I  e  16  but  there  seem  to  be  no  lines 


84  RAYMOND  T.  BIRGE 

at  this  point  resembling  an  e  head.  Again,  however,  the  rough 
theoretical  positions  of  these  two  heads  almost  coincide.  For  the 
other  groups  the  coincidences  are  at  7059.6  and  7887.  The  data 
are  so  inaccurate  here  that  the  positions  will  fit  equally  well  in 
either  of  the  adjacent  band  groups.  Considering  that  we  have  at 
least  approximate  coincidences  at  the  four  points  mentioned  above, 
several  interesting  relations  follow. 

The  values  of  p  and  n  at  these  points  are: 

p       n  p       n  p      n  p       n 

43-50  2  j  43-49  |  40-45  j  34-38 

50-56  /  51-56  3  (  49-53  4  I  44-47 

Since  the  coincidence  is  between  two  heads  of  different  band  groups, 
the  two  values  of  p  —  n  at  each  point  differ  by  unity.  Two  other 
unexpected  facts,  however,  are:  (i)  that  the  discontinuity  in  p 
increases  by  unity  at  each  succeeding  point  of  coincidence;  and 
(2)  that  the  number  of  bands  between  points  of  coincidence  in- 
creases by  four,  from  group  to  group.  This  is  also  shown  in  Fig.  i. 
The  coincident  points  are  indicated  by  vertical  dotted  lines.  The 
length  of  these  lines  gives  the  discontinuity  in  p.  The  number  of 
bands  between  them  is  seen  to  increase  by  four,  as  one  goes  from 
red  to  violet.  In  group  c  there  are  six,  in  d  ten,  and  in  e  fourteen 
bands. 

If  this  rule  were  followed  farther  to  the  red  we  should  expect 
only  two  bands  in  6,  between  the  coincident  bands  46-53  and  43-50. 
This  would  be  the  last  group,  the  next  one,  by  rule,  having  zero 
length.  On  the  violet  side  we  should  expect  nine  more  bands 
(including  the  coincident  ones)  in  the  /  group,  25-28  coinciding 
with  36-38  of  an  unknown  g  group,  and  so  on.  In  the  next  (ti) 
group  the  last  of  the  26  predicted  bands  would  have  />=  —  i,  w=o. 
Since  the  correct  value  of  p— n  for  any  band  group  is  indeterminate 
to  at  least  one  integer,  it  seems  natural  to  suppose  that  all  values 
of  p  should  be  raised  by  one  integer. 

We  should  then  have  a  complete  plan  for  the  First  Deslandres' 
Group.  It  would  start,  theoretically,  at  p  =  o,  w  =  o,  and  would 
consist  of  seven  groups  of  bands.  The  first  head  of  some  band 
near  the  end  of  each  group  would  coincide  approximately  with  the 
first  head  of  a  band  in  the  next  group.  The  number  of  bands 


POSITIVE  BAND  SPECTRUM  OF  NITROGEN  85 

between  coincidences  would  diminish  by  four,  in  each  succeeding 
group.  Some  groups  run  past  the  points  of  coincidence  and  so 
overlap  on  each  other. 

Although  groups  g  and  h  do  not  appear  in  the  ordinary  spectrum, 
Goldstein1  believes  he  has  seen  the  First  Deslandres'  Group,  under 
certain  low-temperature  conditions,  extending  into  the  blue.  Other 
investigators  have  been  unable  to  verify  this.  Group  h  should  start 
at  X  4430  and  extend  to  X  4530.  Group  g  should  extend  from  this 
latter  point  to  X  4890,  and/  from  X  4890  to  X  5442 . 8. 

SECTION  III 

Under  high  dispersion  successive  bands  have  a  very  similar 
appearance,  and  this  not  only  suggested  to  the  author  the  formation 
of  simple  series,  but  also  indicates  the  validity  of  the  von  der  Helm 
arrangement  of  the  bands.  The  general  intensity  of  successive 
bands  also  varies  continuously  through  a  group  of  bands.  All 
simple  series  were  formed  from  lines  of  the  same  general  appearance, 
and  of  a  continuously  varying  intensity.  The  large  number  of 
possible  series  with  approximately  the  same  spacing  is  also  good  evi- 
dence of  a  connection  between  successive  lines. 

A  few  bands  in  group  e  have  been  measured  and  plotted  beneath 
one  another.  It  is  these  bands  (X  59OO-X  5700)  that  indicate  the 
existence  of  some  50  simple  series  of  lines,  superimposed  upon  a 
much  larger  number  of  unrelated  lines.  Below  X  5700  all  of  the  e 
series  die  out,  save  only  those  in  the  first  heads.  In  the  d  group, 
however,  the  series  extend  to  the  last  regular  d  band  at  X  6185,  and 
perhaps  farther.  In  the  case  of  the  /  group  there  seem  to  be  no 
conspicuous  series  save  the  two  mentioned  in  the  first  heads.  This 
portion  is  the  most  irregular  of  the  entire  spectrum. 

The  only  exceptions  to  the  general  rise  and  fall  of  intensity  in 
the  bands  of  one  group  are  two  very  strong  heads  at  X  7072 .8  and 
X  6968.0.  The  latter  lies  at  the  predicted  position  of  I  d  2.  The 
former  lies  somewhat  to  the  red  of  I  c  8.  There  is  no  apparent 
reason  why  either  one  should  be  strong. 

On  the  other  hand,  all  changes  in  appearance  of  the  bands 
under  changing  physical  conditions  point  to  the  Cuthbertson 

1  Goldstein,  Phys.  Zeitschr.,  6,  14,  1905. 


86  RAYMOND  T.  BIRGE 

arrangement  as  the  one  indicating  the  actual  physical  connection 
between  the  sources  of  the  radiation.  Fowler1  has  shown  that  the 
spectrum  of  the  active  modification  of  nitrogen  shows  certain  of 
the  bands  of  the  First  Deslandres'  Group  greatly  intensified,  while 
the  others  are  very  faint  or  entirely  lacking.  The  three  strongest 
bands  are  those  at  X  6253,  X  5804,  and  X  5407  (#  =  46;  ^  =  41,  42, 
and  43),  while  the  weaker  bands  on  each  side  are  those  at  X  6323, 
^5854>  ^5442  (w  =  475  £  =  42,  43>  44)  and  at  X6i85,  X  5755,  and 
X  5373  (#  =  45,  />  =  4O,  41,  and  42).  Fowler  has  pointed  out  this 
evidence  in  favor  of  the  Cuthbertson  arrangement. 

The  fact  that  apparently  the  entire  band  is  increased  in  intensity 
may  point  to  a  further  relation,  not  included  in  the  Cuthbertson. 
It  would  be  very  interesting  to  photograph  this  spectrum  under  high 
dispersion  and  to  note  whether  all  the  lines  of  a  band  were  intensi- 
fied, or  only  those  belonging  in  series. 

Angerer2  has  made  an  exhaustive  study  of  the  First  Deslandres' 
Group  at  low  temperature.  I  have  made  no  critical  study  of  his 
results,  and  cannot  well  do  so  until  I  have  my  own  measurements 
completed.  Several  points,  however,  are  worth  noting. 

At  low  temperature  the  heads  of  a  band  are  far  more  intense, 
relative  to  the  rest  of  the  band,  than  at  ordinary  temperature. 
This  is  especially  true  of  the  III  heads  which,  at  high  temperature, 
escape  detection  in  many  bands — not  having  been  measured  at  all 
by  von  der  Helm.  But  they  are  particularly  strong  at  low  tempera- 
ture. This  would  point  to  an  independence  between  the  series 
lying  within  the  heads  of  the  bands,  and  other  series. 

At  low  temperature  the  entire  spectrum  is  relatively  much 
fainter  than  at  room  temperature.  Aside  from  two  small  groups 
of  lines  in  the  green,  the  only  exceptions  to  this  statement  are  the 
first  heads  of  the  three  bands  X6623,  X  6070,  and  X  5593  (^  =  51; 
£  =  46,  47,  and  48).  The  second  of  these  is  even  more  intense  at 
low  temperature,  while  the  other  two  are  fully  as  intense.  Here 
again  we  have  evidence  in  favor  of  the  Cuthbertson  arrangement. 

There  is  one  additional  fact  pointing  to  a  general  relationship 
between  the  heads  of  all  the  bands.  The  frequency  difference  of 

1  Fowler,  Proc.  Roy.  Soc.,  85  A,  377,  1911. 
3  Ann.  d.  Phys.,  32,  549,  1910. 


POSITIVE  BAND  SPECTRUM  OF  NITROGEN  87 

the  rough  position  of  the  I  and  IV  heads  is  a  constant  for  all  bands 
from  X  5100  to  X  9100,  although  the  length  of  the  bands  more  than 
doubles  within  this  range.  The  maximum  variation  of  the  differ- 
ence is  7  units  (from  2  =  68  to  61).  The  frequency  difference  of  the 
I  and  II  heads,  except  in  the  /  group,  is  also  practically  constant. 
I  cannot  recall  having  previously  seen  this  fact  explicitly  stated. 

This  relation  of  the  heads  is  what  we  should  expect  if  the  bands 
were  composed  of  a  number  of  identical  series  of  lines.  It  seems 
evident  that  all  possible  series  have  very  closely  the  same  spacing, 
but  it  is  also  certain  that  the  spacing  is  not  identical. 

Sections  II  and  III  may  be  summarized  in  the  statement  that 
numerical  relationships  among  the  lines  of  the  First  Deslandres' 
Group  favor  the  von  der  Helm  method  of  grouping,  while  changes 
in  the  bands  under  varying  physical  conditions  of  the  source  all 
point  to  the  Cuthbertson  method  as  the  significant  one. 

CONCLUSIONS 

1.  The  First  Deslandres'  Group  of  the  positive  band  spectrum 
of  nitrogen  consists  really  of  two  spectra,  one  composed  of  a  large 
number  of  superimposed  series  of  lines,  the  other  quite  irregular. 

2.  The  similarity  in  the  spacing  of  all  series  gives  the  banded 
appearance  of  the  spectrum,  the  length  of  a  band  being  the  distance 
between  two  successive  lines  of  each  series. 

3.  The  so-called  " heads"  of  the  bands  are  formed  by  groups 
of  particularly  heavy  lines,   accompanied  by  more  or  less  con- 
tinuous radiation. 

4.  It  is  possible  to  fit  a  greater  number  of  lines  into  the  simple 
series  of  the  von  der  Helm  arrangement  of  bands  than  into  the  more 
complex   two-parameter  formula  indicated  by   the   Cuthbertson 
arrangement.     All  physical  changes  in   the   spectrum,   however, 
favor  the  latter  arrangement. 

5.  Simple  series  of  lines,  running  through  one  band  group  of 
the  von  der  Helm  arrangement,  obey  Deslandres'  Law  for  at  least 
the  first  few  bands,  but  later  show  a  large  and  systematic  deviation 
from  it. 

6.  The   First   and   Second   Progressions   of   the    Cuthbertson 
arrangement  fit  approximately  into  a  formula  containing  both 


88  RAYMOND  T.  BIRGE 

the  second  and  third  powers  of  the  parameter,  but  will  not  fit 
the  simpler  second-power  formula  of  Deslandres'  Law. 

7.  The  successive  band  groups  have  certain  heads  which 
approximately  coincide,  and  these  points  of  coincidence  show 
regularities  which  enable  the  entire  set  of  bands  of  the  First  Des- 
landres' Group  to  be  arranged  so  as  to  indicate  a  definite  plan  for 
the  group. 

The  experimental  part  of  the  investigation  is  the  resolving,  for 
the  first  time,  of  the  39  bands  between  X  5000  and  X  6800  into  about 
6400  lines,  and  the  measurement  of  a  portion  of  these  lines  with  an 
average  error  of  o.oi  A  or  less. 

In  conclusion  the  author  wishes  to  express  his  thanks  to  Pro- 
fessor C.  E.  Mendenhall  for  the  many  helpful  suggestions  offered 
during  the  progress  of  this  investigation. 

DEPARTMENT  OF  PHYSICS 

UNIVERSITY  OF  WISCONSIN 

August  1913 


7  DAY  USE 

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